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 PrimaryHilbertSeries

primary

 Syntax
 ```PrimaryHilbertSeries(I: IDEAL, Q: IDEAL): TAGGED("PSeries") ```

 Description
Let P be a polynomial ring, M the maximal ideal in P generated by the indeterminates, and (Q+I)/I a primary ideal for M/I . This function computes the Hilbert-Poincare' series of (P/I)/((Q+I)/I) .

 Example
 ```/**/ Use S ::= QQ[x,y,z]; /**/ I := ideal(x^3-y*z, y^2-x*z, z^2-x^2*y); /**/ Q := ideal(y, z); /**/ PS := PrimaryHilbertSeries(I, Q); PS; /**/ Use S ::= ZZ/(32003)[x,y,z,w]; /**/ I := ***Ideal(x^5 - yz, y^4 - xz^2, xy^3 - zw, x^2z - yw, /**/ y^2z^2 - w^3, y^3z - x^2w^2, x^3w - z^2, xyw^2 - z^3, /**/ x^3y^2 - w^2, xz^4 - y^2w^3, yz^5 - xw^5, y^3w^5 - z^7, /**/ x^2w^7 - z^8, z^9 - yw^8)***; /**/ Q := ideal(x, y, z); /**/ PS := PrimaryHilbertSeries(I, Q); PS; /**/ \$hp.PSerToHilbert(PS); /**/ Use S ::= ZZ/(32003)[x,y,z]; /**/ I := ideal(S, []); -- ideal in S with no generators /**/ Q := ideal(x, y, z^2); /**/ PS := PrimaryHilbertSeries(I, Q); PS; /**/ \$hp.PSerToHilbert(PS); /**/ HV := \$hp.PSerHVector(PS); -- the H-vector associated to PS /**/ Use S ::= ZZ/(32003)[x,y,z,w]; /**/ I := ***Ideal(-yz + xw, z^3 - yw^2, -xz^2 + y^2w, -y^3 + x^2z)***; /**/ Q := ideal(x, y, z^2, w^3); /**/ PS := PrimaryHilbertSeries(I, Q); PS; /**/ \$hp.PSerToHilbert(PS); /**/ HV := \$hp.PSerHVector(PS); /**/ \$primary.E(0, HV); /**/ [ \$primary.E(J,HV) | J In 0..(\$hp.PSerDim(PS)-2) ]; /**/ [ \$primary.E(J,HV) | J In 0..(len(HV)-1) ]; /**/ Use S ::= ZZ/(32003)[x,y,z,w]; /**/ I := ***Ideal(x^3-y^7, x^2y - xw^3-z^6)***; /**/ Q := ideal(x, y, z, w); /**/ PS := PrimaryHilbertSeries(I, Q); PS; /**/ \$hp.PSerToHilbert(PS); /**/ HV := \$hp.PSerHVector(PS); /**/ [ \$primary.E(J,HV) | J In 0..(\$hp.PSerDim(PS)-2) ]; /**/ [ \$primary.E(J,HV) | J In 0..(len(HV)-1) ]; /**/ Use S ::= ZZ/(32003)[x,y,z]; /**/ I := ideal(z^3); /**/ Q := ideal(x^2, y^2, x*z, y*z); /**/ PS := PrimaryHilbertSeries(I, Q); PS; /**/ \$hp.PSerToHilbert(PS); /**/ HV := \$hp.PSerHVector(PS); /**/ [ \$primary.E(J,HV) | J In 0..(\$hp.PSerDim(PS)-2) ]; /**/ [ \$primary.E(J,HV) | J In 0..(len(HV)-1) ]; ```